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Robben and Ribery, both 34, are out of contract at the end of the season and a primary round of extension negotiations has already begun.
They are part of a group of four players, alongside goalkeeper Sven Ulreich and defender Rafinha, whose contracts expire in June.
“We need some time, then we will make decisions,” Rummenigge told Sky.
“What is required of us is to create a gentle transition.
“We have already made a first (round of talks), when the second will follow, we will see.”
According to daily newspaper Bild, a decision will be made by the end of March at the earliest, leaving the quartet with just a few months to convince the German champions — currently 18 points clear in the Bundesliga — of their continued worth.
Between them Robben and Ribery — part of the team that won the 2013 treble of Champions League, German Cup and Bundesliga — have made nearly 650 appearances for Bayern and scored exactly 250 goals.
However, both are injury prone, especially Ribery, who tore a knee ligament last October.
Yet, when fit, they continue to perform.
Robben scored two late goals in Tuesday’s 6-0 thrashing of minnows Paderborn in the quarter-finals of the German Cup.
Ribery netted a rare Bundesliga goal in Bayern’s 2-0 win at Mainz last Saturday.
Bayern will not want to leave themselves light on the flanks and Kingsley Coman is the only other winger in the squad, although Germany forward Thomas Mueller can play out wide.
Bayern host Schalke in a crunch Bundesliga match on Saturday and face Besiktas in the last 16 of the Champions League in a fortnight.
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